Deviations from normal distributions in artificial and real time series: a false positive prescription

Morris, P. J. ORCID: https://orcid.org/0000-0002-8533-8232, Chakraborty, N. ORCID: https://orcid.org/0000-0002-3134-1946 and Cotter, G. (2019) Deviations from normal distributions in artificial and real time series: a false positive prescription. Monthly Notices of the Royal Astronomical Society, 489 (2). pp. 2117-2129. ISSN 0035-8711 doi: 10.1093/mnras/stz2259

Abstract/Summary

Time-series analysis allows for the determination of the Power Spectral Density (PSD) and Probability Density Function (PDF) for astrophysical sources. The former of these illustrates the distribution of power at various time-scales, typically taking a power-law form, while the latter characterizes the distribution of the underlying stochastic physical processes, with Gaussian and lognormal functional forms both physically motivated. In this paper, we use artificial time series generated using the prescription of Timmer & Koenig to investigate connections between the PDF and PSD. PDFs calculated for these artificial light curves are less likely to be well described by a Gaussian functional form for steep (Γ⪆1) PSD indices due to weak non-stationarity. Using the Fermi LAT monthly light curve of the blazar PKS2155-304 as an example, we prescribe and calculate a false positive rate that indicates how likely the PDF is to be attributed an incorrect functional form. Here, we generate large numbers of artificial light curves with intrinsically normally distributed PDFs and with statistical properties consistent with observations. These are used to evaluate the probabilities that either Gaussian or lognormal functional forms better describe the PDF. We use this prescription to show that PKS2155-304 requires a high prior probability of having a normally distributed PDF, ≥ 0.82, for the calculated PDF to prefer a Gaussian functional form over a lognormal. We present possible choices of prior and evaluate the probability that PKS2155-304 has a lognormally distributed PDF for each.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/119440
Item Type	Article
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > National Centre for Earth Observation (NCEO) Science > School of Mathematical, Physical and Computational Sciences > Department of Meteorology
Publisher	Royal Astronomical Society
Download/View statistics	View download statistics for this item